Understanding the charge transfer effects of single atoms for boosting the performance of Na-S batteries

The effective flow of electrons through bulk electrodes is crucial for achieving high-performance batteries, although the poor conductivity of homocyclic sulfur molecules results in high barriers against the passage of electrons through electrode structures. This phenomenon causes incomplete reactions and the formation of metastable products. To enhance the performance of the electrode, it is important to place substitutable electrification units to accelerate the cleavage of sulfur molecules and increase the selectivity of stable products during charging and discharging. Herein, we develop a single-atom-charging strategy to address the electron transport issues in bulk sulfur electrodes. The establishment of the synergistic interaction between the adsorption model and electronic transfer helps us achieve a high level of selectivity towards the desirable short-chain sodium polysulfides during the practical battery test. These finding indicates that the atomic manganese sites have an enhanced ability to capture and donate electrons. Additionally, the charge transfer process facilitates the rearrangement of sodium ions, thereby accelerating the kinetics of the sodium ions through the electrostatic force. These combined effects improve pathway selectivity and conversion to stable products during the redox process, leading to superior electrochemical performance for room temperature sodium-sulfur batteries.


Revision made:
(Manuscript, page 7) For comparison, a sample with S loading on Ni1-PNC (S@Ni1-PNC) was analyzed by SEM, STEM and EDX mapping analysis (Supplementary Information, Figure S8 and S9), confirming that C, N, S, Ni are welldispersed on the nanosphere with a diameter of ~500 nm.
(Supplementary information)  2. Authors are advised to provide energy absorption maps and corresponding optimized structures for the active sites of Mn1 and Ni1 with respect to polysulfides.
Response: Thanks for your valuable suggestion.The energy adsorption maps and corresponding optimized structures for both Mn1 and Ni1 with respect to polysulfides have been added in the revised Manuscript and revised Supplementary Information.

Revision made:
(Manuscript, page 15) Further, DFT calculations were conducted to evaluate the absorption energies of both Mn1 and Ni1 sites for S8, NaPSs, and short-chain Na2S2 and Na2S.The optimized absorption configurations are shown in Figure S26 and S27 (Supplementary information).As displayed in Figure S26 and S27, the ideal modes consisting of single atom Mn and Ni coordinated with 4 nitrogen atoms are applied in modelling the carbon matrix to calculate the absorption energy of various NaPSs.The energy absorption formula is defined as: E (ad) = E(ad/surf) -E (surf) -E (ad), where E(ad/surf), E(surf), and E(ad) represent the total energies of the adsorbates binding to the surface, cleaning surface, and free adsorbate in gas phase, respectively.Thus, the absorption map in Figure S28 indicates Mn1 sites exhibit stronger absorption abilities for NaPSs than Ni1 sites, suggesting the S conversion reaction on Mn1 sites is kinetically faster than that on Ni1.This is consistent with the speculation from ex-situ XANES spectra.
(Supplementary information)   Response: Thanks for your valuable comment.The density of states (DOS) of both Mn and Ni are provided in the revised Manuscript and Supplementary information.Additionally, Figure S23 is updated to Figure S30 after the correction.

Revision made:
(Manuscript, page 15) To better understand the product-selectivity of Mn1, the correlations between d-band theory on five single-atom metals and their corresponding absorption energies are analyzed in Figure S29.Overall, Mn1 sites possess the strongest absorption abilities for S8 and Na2S among different SA sites, suggesting that Mn1 sites can effectively catalyze S8 molecule cleavage and potentially produce Na2S as the primary reduction product.Moreover, the density of states (DOS) exhibits that the d-band states of Mn1 sites are closer to the Fermi level than these of Ni1 sites (Supplementary information, Figure S30), demonstrating that the antibonding states of Mn1 are less filled than that of Ni1.Accordingly, the relationship between adsorption and the d-band center is negatively correlated (closer to Fermi level), in line with the conclusion of d-band theory.Mn1 sites with the lowest dband center, therefore, possess an increased likelihood of electrons filling the antibonding orbital, which facilitates S molecule cleavage and enhances the S redox kinetics, thus promoting product selectivity toward SC NaPSs (Figure 5f).
(Supplementary information) Figure S30.The density of states (DOS) of both (a) S@Mn1-PNC and (b) S@Ni1-PNC surfaces.4. In the section "Visualization of charge transfer assisted Na ion diffusion", the authors showed that electron transfer has a positive effect on sodium ion diffusion.Therefore, it is necessary to provide the relative energy of sodium ion diffusion when Mn1 is anchored on the matrix.

Response:
We appreciate this great comment from the referee.The relative energy of sodium ion diffusion when Mn1 is anchored on the matrix has been added in the manuscript and supplementary information.

Revision made:
(Manuscript, page 17) Moreover, the electron transfer (ET) effect of Mn1 is revealed by monitoring the relative energy of sodium-ion diffusion on different matrixes (Supplementary information, Figure S31).In contrast to the PNC matrix, the 5.In Figure S14, the unit information is missing on the Y-axis, and the same issue is presented in Figure S20.

Response:
We appreciate the careful review.We have updated Figure S14 and Figure S20 in the Supplementary information.After correction, they are updated to Figure S18 and Figure 24.

Response:
We would like to thank the reviewer for carefully reading.First, the standard electrode potential for Na being ionized to form Na+ is -2.71eV (vs RHE).The onset redox potentials of Na2S6 (long-chain polysulfides) is around 2.1V (versus Na/Na+), which corresponds to -0.61 V (versus reversible hydrogen electrode (RHE)).Additionally, the cutoff discharge voltage is 0.8 V (versus Na/Na+), which corresponds to -1.91 V (versus reversible hydrogen electrode (RHE)).This is why the potential window is set as -0.61eV to -1.91eV (vs.RHE).We have cited several representative works to support this.The corresponding references have been updated at the end of the description.

References:
Response: We would like to thank the reviewer's comment.We have corrected "HAD" to "H(DA)" in this manuscript.

Revision made:
(Manuscript, page 5) H(DA) is the electronic coupling matrix element between donor and acceptor, … (3) It is quite confusing to see that " the re-organization energy depends on the distance " but " it is often treated as a distance-independent".Dependent or independent?Please clarify this.

Response:
We thank for the reviewer's comment.We have corrected this in the manuscript.

Revision made:
(Manuscript, page 5) The re-organization energy depends on the distance between the donor and acceptor (  ) and the solvent polarity (Eq.( 2)).
(4) In the sample preparation of atom probe tomography, more details are needed since it is not easy to prepare a cathode powder sample by the FIB.
Response: Thank you for your suggestion.Preparing atomic probe tomography (APT) powder samples is more challenging than preparing bulk samples.The key difference is that, prior to FIB cutting, deposited Pt must cover not only the top of the powder sample but also the surrounding area of the powder sample.In contrast, for bulk samples, Pt only needs to be deposited on top of the bulk material.Detailed steps for preparing APT samples using FIB have been added in the revised supplementary information for the convenience of the readers.

Revision made:
(Supplementary information, Experimental section) Sample preparation for Atom probe tomography (APT) measurement.To prepare samples for the atomprobe experiments, the S@Mn1-PNC nanospheres were cleaned and dried on a Si substrate (sample stage) and sputter coated with Cr in a sputter coater.After coating, specimens were transferred into a focus ion beam (FIB) system, where a strip of Pt was deposited on the top and surrounding area of the powder samples by using electron-assisted chemical vapor deposition.Afterwards, a microscope or SEM (scanning electron microscope) was performed to check the surface of the samples and mark the characterization positions.An FEI Quanta 200 3D FIB instrument was utilized to extract the samples . 1 This process involves cleaning the surrounding material to create a cantilevered area, followed by using a nano-hand to extract and cut it into multiple block samples from the prefabricated silicon base.During sample preparation, careful attention was paid to avoid damage from the Ga + focused ion beam, with ion energies kept below 10 keV after the lift out. 2 In addition, the sample's surface tends to accumulated impurities and residue during etching, thus necessitating thorough cleaning to ensure a smooth and high-quality surface.a current density of 0.2 A g -1 , the S@Mn1-PNC cathode retains the highest capacity of 784.6 mAh g -1 amongst all the S@Mn1-PNC samples (Figure 3d), which also represents the highest capacity retention of 84%.
(Manuscript, page 10) Overall, single atom catalysts exhibit distinct electrocatalytic activities towards the high-plateau and lowplateau conversion regions, showing different pathway selectivity.Meanwhile, the S@Mn1-PNC and S@Fe1-PNC cathodes demonstrate high reaction kinetics and excellent battery performance via effectively catalyzing the rate-determining step.
(6) In figure 4c and d, the text in scale bar is too small to read while the text in figure 4g/h is too big.

Response:
We thank the reviewer's careful reading.We increased the size in scale bar in figures 4c and 4d, while we decreased the size of the text in figures 4g and 4h in the manuscript.In addition, some axis labels are missing in Figure 4c and d.Accordingly, we added arrows from the surface to the interior in Figure 4c and Figure 4d, indicating that both Na and S are distributed throughout the bulk of the electrode.

Revision made:
(Manuscript, page 12) of secondary ion fragments obtained from the S@Mn1-PNC electrode after 50 cycles.(f) k 3 -weighted FT-EXAFS curves of S@Mn1-PNC in R-space during the initial discharge and charge processes.WT plots of the Mn k-edge of S@Mn1-PNC cathode during (g) discharge and (h) charge processes.

Responses to Reviewer #3:
This study provides a comprehensive and insightful exploration of the electronic structures of single-atom catalysts (SACs) in the context of room temperature (RT) sodium-sulfur (Na-S) batteries.It effectively integrates machine learning (ML) techniques and density functional theory (DFT) calculations to establish a clear correlation between the electron capture and donation capabilities of various SACs and their respective product selectivity during charge and discharge processes.This manuscript can be considered for publication after addressing the following questions: We are very grateful for the in-depth and constructive comments and suggestions from the reviewer.We have revised the manuscript according to the reviewer's comments.All changes have been highlighted in the revised manuscript and supporting information files.
(1) The reviewer is confused about the necessity of adoption of machine learning techniques since the choice of different kinds of single-atom metals are limited.And the results could also be obtained through the DFT calculation.The reviewer suggests the author further explain the necessity of adopting the ML method.
Response: We thank the reviewer for this important question.Indeed, machine learning can give us a map that consists of energy differences and bond lengths between sulfur and metal.By combining this with knowledge of sodium-sulfur battery theory, we can quickly identify a specific area where a potential efficient catalyst may exist (as shown in Figure 1d).Nevertheless, this cannot be obtained by DFT calculations.Furthermore, Machine learning can integrate more scientific descriptors, making it simpler for researchers to pinpoint the most relevant descriptors quickly, filtering out the most effective materials.For instance, by utilizing the RandomForest method on 10 randomized data sets, we can swiftly identify the "Lms" 11 features, as illustrated in Figure S1.These features, determined by Pearson and Spearman methods, are closely linked to adsorption energy (Eds), aiding us in promptly identifying suitable sulfur cathode catalysts for sodium-sulfur batteries in our subsequent research alongside theory.In addition, while DFT simulations can evaluate the electrochemical performance of all metal monatomic structures, employing various machine learning algorithms for multidimensional correlation analysis and prediction of DFT-calculated datasets not only helps us recognize patterns of different physical and chemical properties' impact on adsorption or reaction energy but also allows for algorithm optimization with strong predictive capabilities through cross-correlation learning of numerous influencing descriptors.This optimized approach enables the prediction of potentially highly active metal atoms suitable for such reactions, a task that DFT simulations cannot achieve directly.

Revision made:
(Supplementary information) (2) The paper emphasized the application of ML in their research, but my feeling is that the authors only used some very rudimentary algorithms for fitting their results.ML did not show its power.I agree that the authors studied a fundamental problem.I also agree that ML + DFT is a quite exciting topic, but I cannot agree that this study used ML in a necessary and useful way.As a result, the ML aspect of this paper did not provide any insight for the readers.

Response:
We appreciate the reviewer for bringing up this important point.Firstly, it is crucial to highlight that this work is centered on actively delving into the field of sodium-sulfur batteries.In the presenting work, we only have access to fewer than 20 individual atomic metals to select from the periodic table.This is the reason that the presented datasets are not as many as in other ML works.Understand this circumstance, we agree with the reviewer's concern that our current work may not fully exploit the power of machine learning for big data analysis.To avoid misunderstanding, we have made corresponding revisions in this article, including title, abstract, introduction and section 1.The revisions include two parts: increase the weight of experimental conclusions and optimize the number of ML dataset.The changes aim for readers to understand that our focus is primarily on the experimental exploration and identification of which single-atom's physical properties are crucial indicators for the selectivity of sulfur cathode products.However, we still believe that the machine learning in this article is an inspiring tool to build and screen the most suitable single atom catalysts for electron transfer and the lowest M-S bond energy with combination of our theoretical knowledge in sodium-sulfur batteries, to achieve the optimal discharge product (short-chain polysulfides).In particular, the experimental demonstration results and the ML prediction results are well consistent.
To increase accuracy, we extend the current 69 DFT simulation cases to 123 cases by adding a new structure M-N3C into the presenting work.A quick note to emphasize the necessity of ML is that the ML can quickly identify the best scientific descriptors for evaluating the effects of various physical and chemical properties of the metal atoms in sodium sulfur batteries (as seen in Figure S1) and make predictions.This unique and important feature cannot be provided by DFT calculations.

Understanding the charge transfer effects of single atoms for boosting the performance of Na-S batteries (Manuscript, page 1)
The establishment of the synergistic interaction between the adsorption model and electronic transfer helps us achieve a high level of selectivity towards the desirable short-chain sodium polysulfides during the practical battery test.
((Manuscript, page 3) In this study, we first construct the collaborative relationship between the absorption model and electron transfer.This method can help us rapidly screen out promising single atom catalysts that have a high level of selectivity towards the short-chain sodium polysulfides for sodium sulfur batteries.
(Manuscript, page 6) Next, machine learning is performed as a sufficient way to identify the best scientific descriptors, which can assess how various physical and chemical properties of metal atoms affect adsorption or reaction energy.As shown in Figure S1, it is obviously that the bond length of metal and sulfur can influence the adsorption and reaction energy.According to the prediction in Figure 1e, a linear relationship between the adsorption energy Eads and diverse SACs is obtained, which demonstrates that the prediction results of ML are like those of DFT calculations.Then, by establishing a linear relationship between the lengths of adsorption and metal-sulfur bonds (Figure 1d), combined with the theoretical knowledge discussion, we can rapidly screen potential SACs for Na-S batteries that should exist in a specific region (as shown as Figure 1d, optimized region), in which the SACs, Mn-N4, Fe-N4, Rh-N4, Mg-N4, Co-N4 and Mg-C1N3 feature mild adsorption (more detailed machine learning procedures are in the Supplementary information, Figure S2, Figure S3, Figure S4 and Table S2, Table S3, Table S4, Table S5).With the assistance of prediction, we selected six representative SACs, Mn1, Fe1, Co1, Sn1, Cu1, and Ni1, which were used to conduct further experimental validation in Na-S batteries.
(Supplementary information, experimental section) It is known that most correlations between the descriptors and targets were probably nonlinear in electrocatalytic and photocatalytic reactions.Herein, four types of nonlinear ML algorithms except linear regression (LR) algorithm were used to predict the adsorption activity in this work, including tree ensemble methods (RFR and GBR), and kernel methods (SVR and KRR) algorithms.The model performances of LR, RFR, GBR, SVR and KRR were compared by the root-mean-square error (RMSE) via k-fold cross validation (20-fold used in this case).The DFT dataset was randomly split into training and test sets, where 10% of the dataset is divided as a test set, and the other of the dataset becomes a train set.For a better machine learning (ML) performance, the standardization of target values was applied to our input dataset.In addition, after a rough screening to features according to the degree of feature importance, the 11 main features (Table S1) are chosen as descriptors.Package sklearn was employed to implement the data processing and import the ML algorithms.LR: linear regression; RFR: random forest regression; GBR: gradient boosted regression; SVR: support vector regression; KRR: Kernel ridge regression       After analyzing the resultss, the predicted performance of the five ML algorithms was evaluated, in which SVR and KRR algorithms show distinct overfitting with relatively large or zero RMSE (Figure S3a and S3b).
Consequently, the other three algorithms were mainly used to observe the fitting results, and it was found that GBR algorithm (vs.RFR and LR algorithm, Figure 1e, Figure S2a, S2b and Table S3, Table S4) gives a much better fitting.Then, the dataset was split into training and learning sets over the same 20 repeated and randomized data for ML prediction.Similar with fitting results, LR algorithm shows a poor prediction, with the R 2 and RMSE values of the training/testing sets are 0.759 and 0.435 eV, respectively (Figure S4a).The testing set with RFR algorithm exhibits a better prediction performance than the training set, with the R 2 of 0.969 and RMSE of 0.156 eV (Figure S4b).S4c).The average errors of RMSE and MSE for LR, RFR and GBR algorithms over 20 times of random training and learning are shown in Figure S5 and Table S5.Both RFR and GBR algorithms give a lower error bar of RMSE/MSE than LR algorithm, consistent with the model prediction results.According to the prediction in Figure 1e, a linear relationship between the adsorption energy Eads and diverse SACs is obtained, which demonstrates that the prediction results of ML are like those of DFT calculations.Meanwhile, compared to DFT calculations, machine learning can accelerate the collection of large numbers of computational results.
(3) Please clarify the size and structure of the data used for ML training.Is it only 69 simulation cases?
Response: Thank you for the reviewer's question.Yes, there are 69 simulation cases in the first draft.The reason that the number of simulation cases is lower than the typical ML training is the limited metal elements that can construct a M-N4 structure.To increase the generality of our simulation, we have extended the simulation cases from 69 to 123 DFT calculation datasets by adopting the M-N4 and M-C1N3 structure in the revised manuscript.We understand that machine learning typically benefits from larger datasets, and we have made efforts to expand the DFT calculation dataset in the last two months.We excluded metal types that could not reliably form the M-N4 and M-C1N3 structure, resulting in a suitable database that we believe provides a reasonable input for enhancing the accuracy of analysis and predictions.The changes made in this work can be found in the response to the Comment #2.
(4) More details are needed to evaluate the authors' work on ML.It is currently not convincing at all.

Response:
We really appreciate this comment from the reviewer.To make this work more convinced, we supplemented more DFT data as discussed above.At the same time, we changed the k value and the training/testing samples, increasing the test set.In addition, to emphasize that ML is one of the steps in predicting efficient catalysts, we adjust the ML part in the article, and more details about the ML procedures have been moved in the supplementary information.Just a quick note to emphasize the importance of this work.Although we can not provide datasets as many as a typical ML simulation, we have tried our best to construct DFT models by using the only 19 metals that are able to form single atoms.This work is the first one to build scaling relationship between single atoms catalysts and product selectivity in sodium-sulfur batteries.This work aims to inspire future research in the field of sodium-sulfur batteries, and we believe that upcoming work will further enhance machine learning models and data volume.

Revision made:
(Manuscript, page 6) Next, machine learning is performed as a sufficient way to identify the best scientific descriptors, which can assess how various physical and chemical properties of metal atoms affect adsorption or reaction energy.As shown in Figure S1, it is obviously that the bond length of metal and sulfur can influence the adsorption and reaction energy.According to the prediction in Figure 1e, a linear relationship between the adsorption energy Eads and diverse SACs is obtained, which demonstrates that the prediction results of ML are like those of DFT calculations.Then, by establishing a linear relationship between the lengths of adsorption and metal-sulfur bonds (Figure 1d), combined with the theoretical knowledge discussion, we can rapidly screen potential SACs for Na-S batteries that should exist in a specific region (as shown as Figure 1d, optimized region), in which the SACs, Mn-N4, Fe-N4, Rh-N4, Mg-N4, Co-N4 and Mg-C1N3 feature mild adsorption (more detailed machine learning procedures are in the Supplementary information, Figure S2, Figure S3, Figure S4 and Table S2, Table S3, Table S4, Table S5).With the assistance of prediction, we selected six representative SACs, Mn1, Fe1, Co1, Sn1, Cu1, and Ni1, which were used to conduct further experimental validation in Na-S batteries.
(Supplementary information, Experimental section) Machine Learning (ML) Methods.A method combining density functional theory (DFT) calculations with machine learning (ML) by using the bond length of M-S and the adsorption energies of the metal with sulfur, Na2S, and Na2S4 as indicators to predict advanced single atom catalysts for high-performance RT Na-S batteries.
Here, a total of 123 adsorption energies of different MN4 and MC1N3 sites were obtained by DFT calculations and 123 available DFT data (with the consideration of the stability of materials and thereby deleting the data with broken structures) were used for machine training and learning in five ML models (i.e.linear regression (LR), random forest regression (RFR), gradient boosted regression (GBR), support vector regression (SVR), and Kernel ridge regression (KRR) algorithms) coupling with the elemental information.The relationships between the used descriptors and adsorption activity were firstly analyzed through the Pearson correlation coefficient (Pearson), the Spearman correlation coefficient (Spearman) and the RandomForest feature importance (RandomForest) methods, as shown in Figure S1 and Table S2.The rankings of these descriptors by Pearson are basically consistent with that by Spearman, except for the metal-sulfur bond (Lms), whereas RandomForest method displays obviously distinction although the top two rankings are same with Spearman method.The rankings indicate that adsorption energies to polysulfides and sodium sulfide exhibits low correlations with most descriptors except the change of metal-nitrogen bond length (D_Lmn), Lms and valence electron number of metal element (Nve) and adsorbed species (Ms).After a rough screening of features according to the degree of feature importance, 11 main features (Figure S1) were chosen as descriptors.The sklearn package was employed to implement the data processing and import the ML algorithms.After analyzing the importance of features, the predicted performance of the five ML algorithms was evaluated, in which SVR and KRR algorithms show distinct overfitting with relatively large or zero RMSE (Figure S3a and S3b).Consequently, the other three algorithms were mainly used to observe the fitting results, and it was found that GBR algorithm (vs.RFR and LR algorithm, Figure 1e, Figure S2a, S2b and Table S3, Table S4) gives a much better fitting.Then, the dataset was split into training and learning sets over the same 20 repeated and randomized data for ML prediction.Similar with fitting results, LR algorithm shows a poor prediction, with the R 2 and RMSE values of the training/testing sets are 0.759 and 0.435 eV, respectively (Supplementary information, Figure S4a).The testing set with RFR algorithm exhibits a better prediction performance than the training set, with the R 2 of 0.969 and RMSE of 0.156 eV (Supplementary information, Figure S4b).Table S4.Eds from the DFT calculations and the full-fit results using the three ML algorithms, LR, RFR and GBR, respectively.Response: Accordingly, we have added the missed label in Figure 4a.In addition, we added arrows from the surface to the interior in Figure 4c and Figure 4d, indicating that both Na and S are distributed throughout the bulk of the electrode.

Figure S26 .
Figure S26.The adsorption configurations of Mn1 to different polysulfides derived from DFT calculations.

Figure S27 .
Figure S27.The adsorption configurations of Ni1 to different polysulfides derived from DFT calculations.

Figure S28 .
Figure S28.Adsorption energies of polysulfides on the active sites of Mn1 and Ni1.
Figure S31.(a) the relative energy of sodium-ion diffusion on PNC and Mn1-PNC with Mn1 anchored on the matrix.(b) Schematic model of Na + diffusion path on PNC matrix.(c) Schematic model of Na + diffusion path on Mn1-PNC matrix.

Figure S24 .
Figure S24.Time of flight-secondary ion mass spectroscopy (TOF-SIMS) images collected at various depths from the cathode surface of S@Mn1-PNC illustrate the S and Na after 50 cycles.

Figure 4 .
Figure 4. Pathway selectivity and cycling stability mechanism.(a) In-situ synchrotron-based XRD patterns of S@Mn1-PNC.(b) Ex-situ X-ray absorption spectra of S for S@Mn1-PNC during the initial cycle.(c) and (d) 3D reconstructed images of TOF-SIMS depth profiles of Na and S after 10 cycles.(e) Normalized depth profiles

Figure S1 .
Figure S1.Importance of used 11 features through the RandomForest method over the 10 randomized data, and Pearson and Spearman methods.
Figures and Tables adsorption energies to polysulfides and sodium sulfide exhibits low correlations with most descriptors except the change of metal-nitrogen bond length (D_Lmn), Lms and valence electron number of metal element (Nve) and adsorbed species (Ms).After a rough screening of features according to the degree of feature importance, 11 main features (FigureS1) were chosen as descriptors.The sklearn package was employed to implement the data processing and import the ML algorithms.

Figure S2 .
Figure S2.Comparison of the adsorption energy (Eds) from the DFT calculations and the full-fit results using the various ML algorithms: (a) RFR and (b) LR, respectively.R 2 : coefficient of determination; RMSE: root mean square error.

Figure S1 .
Figure S1.Importance of used 11 features through the RandomForest method over the 10 randomized data, and Pearson and Spearman methods.

Figure S2 .
Figure S2.Comparison of the adsorption energy (Eds) from the DFT calculations and the full-fit results using the various ML algorithms: (a) RFR and (b) LR, respectively.R 2 : coefficient of determination; RMSE: root mean square error.

Figure S4 . 5 .
Figure S4.Average MSE/RMSE values of LR, RFR, and GBR over the same 20 repeated and randomized data, respectively.

Figure 4 .
Figure 4. Pathway selectivity and cycling stability mechanism.(a) In-situ synchrotron-based XRD patterns of S@Mn1-PNC.(b) Ex-situ X-ray absorption spectra of S for S@Mn1-PNC during the initial cycle.(c) and (d)3D reconstructed images of TOF-SIMS depth profiles of Na and S after 10 cycles.(e) Normalized depth profiles of secondary ion fragments obtained from the S@Mn1-PNC electrode after 50 cycles.(f) k 3 -weighted FT-EXAFS curves of S@Mn1-PNC in R-space during the initial discharge and charge processes.WT plots of the Mn k-edge of S@Mn1-PNC cathode during (g) discharge and (h) charge processes.

Table S1 .
List of DFT-calculated and elemental features used as descriptors.

Table S2 .
Values of important 11 features through the RandomForest method over the 10 randomized data, and Pearson and Spearman methods.S and the adsorption energies of the metal with sulfur, Na2S, and Na2S4 as indicators to predict advanced single atom catalysts for high-performance RT Na-S batteries.Here, a total of 123 adsorption energies of different MN4 and MC1N3 sites were obtained by DFT calculations and 123 available DFT data (with the consideration of the stability of materials and thereby deleting the data with broken structures) were used for machine training and learning in five ML models (i.e.linear regression (LR), random forest regression (RFR), gradient boosted regression (GBR), support vector regression (SVR), and Kernel ridge regression (KRR) algorithms) coupling with the elemental information.The relationships between the used descriptors and adsorption activity were firstly analyzed through the Pearson correlation coefficient (Pearson), the Spearman correlation coefficient (Spearman) and the RandomForest feature importance (RandomForest) methods, as shown in FigureS1and TableS2.The rankings of these descriptors by Pearson are basically consistent with that by Spearman, except for the metal-sulfur bond (Lms), whereas RandomForest method displays obviously distinction although the top two rankings are same with Spearman method.The rankings indicate that

Table S3 .
Feature values for metal elements in ML modelling, including atomic number of metal element, period number of metal element, the group of metal element, bulk wigner-seitz radius of metal element, valence electron number of metal element, atomic mass of metal element, electronegativity of metal element, density of metal element.

Table S4 .
Eds from the DFT calculations and the full-fit results using the three ML algorithms, LR, RFR and GBR, respectively.
Figure S4.Average MSE/RMSE values of LR, RFR, and GBR over the same 20 repeated and randomized data, respectively.TableS5.The average MSE/RMSE value of LR, RFR and GBR over the same 20 repeated and randomized data.
It may indicate that the predicted Eds values present a deviation from the actual Eds values and prediction of RFR overestimated Eds.Corresponding to a better fitting result, GBR algorithm presents a relatively accurate prediction with the R 2 and RMSE values of the training/testing sets are 0.97 and 0.153 eV, respectively (Figure

Table S1 .
It may indicate that the predicted Eds values present a deviation from the actual Eds values and prediction of RFR overestimated Eds.Corresponding to a better fitting result, GBR algorithm presents a relatively accurate prediction with the R 2 and RMSE values of the training/testing sets are 0.97 and 0.153 eV, respectively(Supplementary information, FigureS4c).The average errors of RMSE and MSE for LR, RFR and GBR algorithms over 20 times of random training and learning are shown in FigureS5and TableS5.Both RFR and GBR algorithms give a lower error bar of RMSE/MSE than LR algorithm, consistent with the model prediction results.According to the prediction in Figure1e, a linear relationship between the adsorption energy Eads and diverse SACs is obtained, which demonstrates that the prediction results of ML are like those of DFT calculations.Meanwhile, compared to DFT calculations, machine learning can accelerate the collection of large List of DFT-calculated and elemental features used as descriptors.

Table S2 .
Values of important 11 features through the RandomForest method over the 10 randomized data, and Pearson and Spearman methods.

Table S3 .
Feature values for metal elements in ML modelling, including atomic number of metal element, period number of metal element, the group of metal element, bulk wigner-seitz radius of metal element, valence electron number of metal element, atomic mass of metal element, electronegativity of metal element, density of metal element.